In the early 1960's, Arpad Elo developed the Elo rating system.
It was the first rating system that had probabilistic underpinnings. Originally, Elo developed it for the game of chess, and chess federations around the world adopted it quickly. It became popular and common for many other games too, including Go, Scrabble, table tennis, etc.
Game federations do not use identical (parameters for) rating systems. They attach different titles to a rating, and they have different rule sets to determine an initial rating for new participants.
Usually, an average amateur player's rating ranges between 1300 and 1700 Elo points.
U.S. Chess Federation's classes are:
Elo rating class members ----------- ------- ------- 2200 - 2800 Master 4 % 2000 - 2200 Expert 8 % 1800 - 2000 Class A 12 % 1600 - 1800 Class B 18 % 1400 - 1600 Class C 18 % 1200 - 1400 Class D 20 % 0 - 1200 Class E 20 %
International Chess Federation's top ratings are:
Elo rating title ----------- -------------------------- 2650 - 2800 world champions 2500 - 2650 international grandmasters
The rating indirectly represents the probability of winning against other rated players. This probability depends only on the difference between the two players' ratings as follows:
rating probability difference of winning ---------- ----------- 400 .919 300 .853 200 .758 100 .637 50 .569 0 .500 -50 .431 -100 .363 -200 .242 -300 .147 -400 .081
This represents the area under the standard bell-shaped curve where 200 * sqrt(2) points are taken as one standard deviation. The table shows some sample points on this curve, adequate for good approximations of rating calculations by interpolation.
One method is: A new participant plays three initial games against opponents with already established ratings. These games, for example, account as:
These initial game results are averaged and used for the new member's initial rating.
Example: A new member loses a game against a 1700-opponent, draws against a 1400-opponent and wins against a 1300-opponent. The result is an initial rating of 1467 = ( (1700-200) + 1400 + (1300+200) ) / 3.
The Elo system can be modified to implement Go ranks at a Go server.
Internally, DGS uses:
Points Go rank ------ ------- 2300 3 dan 2200 2 dan 2100 1 dan
2000 1 kyu 1900 2 kyu 1800 3 kyu
1500 6 kyu 1000 11 kyu 500 16 kyu 0 21 kyu
-100 22 kyu -200 23 kyu -300 24 kyu
Tim Brent: Originally 2000 in the Chess rating was a base point, based upon a 50% score at the US Open. The original idea was using Chess to find out if mental activity decreases with aging.
Frs: What does the Elo rating system have to do with an age-dependent decrease of mental activity?
Tim Brent: He had a theory that you could use success in chess as a basis for showing the effects of aging on mental activity, i.e. a player who could play at a 2400 level in his forties is now playing in his fifties at a 2260 level. Could it be proof that his cognitive ability went down 6 percent over that period? (Of course this theory doesn't consider that the aforementioned player might simply have started losing against a group of stronger players.)
The ELO rating depth also states something over the depth of the game. The total depth of a game is defined by two end points of the range of skills: the total beginner and the theorethical best play by an unfallible, allmighty creature.
Both are not easy to establish: Is someone already a beginner who just heard the rules, thereby setting the lowest standard or does it need several games until one has immersed the rules of a game and is able to play on its own? On the other end of the range on simply has to take the best player at a given time. The total beginner, yet playing on its own according to the simple rules can in Go safely be set at 30 kyu. Theoretical best play could result in the strength of an imaginable 13 dan according to measurements of standard deviations among professional games.
Only taking 20 kyu and 9 dan as endpoints makes Go until now the deepest game. A rating difference of 2900 ELO points from Gu Li to a 20 kyu with 100 ELO points is a difference in insight into the game by 29 times the standard deviation (100 ELO points).
Chess in comparision has a similar endpoint (Gari Kasparow with once 2851 points, s.a.), yet the standard deviation is set at 200 ELO points. More difficult to compare due to the draws, however it results in a depth of Chess of (only) 14 layers of standard deviation if the total beginner in Chess had a rating of zero ELO points (which s?he has not AFAIK).